Question

The ${\mathbf{8}}^{\mathbf{t}\mathbf{h}}$ grade science class is going to the zoo. The class can spend up to $\mathit{\backslash (}\mathbf{300}$admission.

Zoo Admission
Visitor	Cost
Student	$\mathbf{\backslash )}\mathbf{8}$
Adult	$\mathbf{\$}\mathbf{10}$

a. Write an inequality for this situation.

b. If there are students in the class and adults will attend for every student, how much will admission be?

Short answer

1. The inequality for this situation is $\mathbf{8}\mathit{x}\mathbf{+}\mathbf{10}\mathit{y}\mathbf{\le }\mathbf{300}$.
2. The number of admissions will be $\mathbf{36}$.

Step-by-step solution

Step1. Observe the given table.

The given table is:

Zoo Admission
Visitor	Cost
Student	$\$8$
Adult	$\$10$

From the given table, it can be noticed that cost of $1$admission of the student is and the cost of $1$admission of $1$the adult is $\$10$.

Step 2. Write an inequality for this situation.

The inequality for the given situation is:

Let $x$, $y$be the number of students and adults respectively.

The cost of 1 admission of the student is and cost of admission of 1 adult is $\$10$.

Therefore, the cost of admission of $x$students and $y$adults is given by $8x+10y$.

The class can spend up to $\$300$admission. Therefore, that implies:

$8x+10y\le 300$

Therefore, the inequality for this situation is $8x+10y\le 300$.

Step 3. Calculation

It is given that the cost of 1 admission of the student is and cost of 1 admission of 1 adult is $\$10$.

It is also given that there are students in the class and 1 adult will attend for every $8$student.

If there are $8$students, $1$the adult will be there.

If there is $1$a student, $\frac{1}{8}$the adult will be there.

Therefore, if there are $32$students, then:

$\frac{1}{8}\times 32\text{\hspace{0.17em}adults}=4\text{adults}$

Therefore, the number of admissions is given by:

$32+4=36$

Therefore, the number of admissions will be $36$.